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1.
The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, Nc, Nq and Nγ are presented as a function of soil internal friction angle (ϕ) and the ratio (ri/ro) of inner to outer radii of the footing.  相似文献   

2.
We studied the upper-bound ultimate bearing capacity of smooth strip shallow footings with symmetrical and asymmetrical horizontal confinements on purely frictional sand within the framework of upper-bound limit analysis. The subsoil follows the associated flow rule, and no surcharge on the soil surface is assumed. The contact between the soil and the horizontal confinement walls is assumed to be perfectly rough. The upper-bound solutions for the objective functions are obtained using nonlinear sequential quadratic programming. The results for the different internal friction angles φ are provided in terms of the variation of two parameters, namely, the bearing capacity factor Nγ and the correction factor of bearing capacity Kγ, with respect to the change in the clear spacing between the edge of smooth footing and the rigid vertical walls. The values of Nγ and Kγ increase with φ and decrease with the clear spacing between the edge of the smooth footing and the rigid vertical walls. Nγ and Kγ are more sensitive to this confining effect as φ increases. The numerical results, a comparative analysis with the results from previous studies, and design charts are also included.  相似文献   

3.
In this research, the reliability analysis of seismic ultimate bearing capacity of strip footing is assessed with implementing slip lines method coupled with random field theory. The probability density functions of seismic and static bearing capacities which are log-normal and nearly normal distribution respectively are compared to each other. The predicted Probability Density Function (PDF) of the seismic bearing capacity by slip line method is verified, with those of the Terzaghi equation and Monte Carlo simulation (MCs). For uncertainties analysis by Terzaghi equation the Nc, Nq and Nγ are assessed stochastically.  相似文献   

4.
In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (quE) is expressed in terms of single coefficient NγE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (df/B0), seismic acceleration (kh, kv) are studied on the variation of seismic bearing capacity co-efficients.  相似文献   

5.
The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors Nσ0 and Nσ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.  相似文献   

6.
Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors Nq and Nγ and of the shape factors sq and sγ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.  相似文献   

7.
By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξγ) was determined, where ξγ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξγ at S/B = 0 becomes equal to 2.0, and the maximum ξγ occurs at S/B = Scr/B. For S/B?Scr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>Scr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξγ for S/B>Scr/B. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

8.
A three-dimensional kinematic limit analysis approach based on the radial point interpolation method (RPIM) has been used to compute collapse loads for rectangular foundations. The analysis is based on the Mohr-Coulomb yield criterion and the associated flow rule. It is understood that the internal plastic power dissipation function and flow rule constraints can be expressed entirely in terms of plastic strain rates without involving stresses. The optimization problem has been solved on basis of the semidefinite programming (SDP) by using highly efficient primal-dual interior point solver MOSEK in MATLAB. The results have been presented in terms of the variation of the shape factors with changes in the aspect ratio (L/B) of the footing for different values of soil internal friction angle (ϕ). Computations have revealed that the shape factors, sc and sq, due to effects of cohesion and surcharge increase continuously with (1) decrease in L/B and (2) increase in ϕ. On the other hand, the shape factor sγ, due to the effect of soil unit weight, increases very marginally with an increase in L/B up to (1) ϕ = 25° for a rough footing and (2) ϕ = 35° for a smooth footing. Thereafter, for greater values of ϕ, the variation of sγ with L/B has been found to be quite similar to that of the factors sc and sq. The variations of (1) nodal velocity patterns, (2) plastic power dissipation, and (3) maximum plastic shear strain rates have also been examined to interpret the associated failure mechanism.  相似文献   

9.
By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor Nγ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance Bt from the footing edge. For a given footing width (B), the value of Bt increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, Bt/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of Nγ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

10.
The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time, is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor (ξγ), due to the component of soil unit weight, is computed with respect to changes in the clear spacing (S) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of ξγ for the smooth footings are found to be always lower than the rough footings. The values of ξγ are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of ξγ.  相似文献   

11.
The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξγ was found to increase continuously with a decrease in S/B, where (i) ξγ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξγ was found to be very extensive for small values of S/B; ξγ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

12.
A kinematic method of slices has been used in this article to deal with the stability problems of strip foundations subjected to uplift loads. The method is based on the upper bound theorem of limit analysis and satisfies the kinematic admissiblility of the chosen collapse mechanism. Assuming the global rupture surface as an arc of logarithmic spiral, uplift factors Fc, Fq and Fγ separately for the effects of cohesion, surcharge and density have been determined. The effect of the yielding of soil mass with partial soil shear strength parameters along the slice interfaces on the results has been examined. The ultimate uplift capacity increases with increase in soil shear strength along the interfaces of slices. The results compare reasonably well with the various existing theories and reported experimental tests data. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

13.
The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N q and N = bearing capacity factors for a semi-infinite layer - N qs and N s= bearing capacity factors for a finite layer - H o /B= limiting depth - D r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q u= bearing capacity - = unit weight of sand  相似文献   

14.
A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footing–soil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in ?, and (iii) becomes almost negligible beyond S/B > 3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

15.
This study evaluates the failure modes and the bearing capacity of soft ground reinforced by a group of floating stone columns. A finite difference method was adopted to analyze the performance of reinforced ground under strip footings subjected to a vertical load. The investigation was carried out by varying the aspect ratio of the reinforced zone, the area replacement ratio, and the surface surcharge. General shear failure of the reinforced ground was investigated numerically without the surcharge. The results show the existence of an effective length of the columns for the bearing capacity factors N c and N γ. When certain surcharge was applied, the failure mode of the reinforced ground changed from the general shear failure to the block failure. The aspect ratio of the reinforced zone and the area replacement ratio also contributed to this failure mode transition. A counterintuitive trend of the bearing capacity factor N q can be justified with a shift in the critical failure mode. An upper-bound limit method based on the general shear failure mode was presented, and the results agree well with those of the previous studies of reinforced ground. Equivalent properties based on the area-weighted average of the stone columns and clay parameters were used to convert the individual column model to an equivalent area model. The numerical model produced reasonable equivalent properties. Finally, a theoretical method based on the comparison of the analytical equations for different failure modes was developed for engineering design. Good agreement was found between the theoretical and numerical results for the critical failure mode and its corresponding bearing capacity factors.  相似文献   

16.
By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, ηc and ηγ, to be multiplied with Nc and Nγ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

17.
ABSTRACT

Probabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, Nγ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on Nγ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor Nγ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic Nγ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between Nγ and the friction angle.  相似文献   

18.
Ring footings are widely used to support structures like silos and storage tanks. Analytical design of safe and economical shallow footings requires the knowledge of the bearing capacity factors N’c and N’γ. The geotechnical design Eurocode 7 provides such factors only for simple geometric shapes like squares, circles or rectangles. Furthermore the N’γ factor has been extensively carried out but the research on the N’c factor hasn’t yet been performed. Thus, the present study aims to provide the first numerical N’c values of a ring footing laying on general c-φ Mohr-Coulomb soil. The results, carried out by using FLAC code, indicate that for rough footings there is an optimal ring which is also dependent of the friction φ. The optimal value of ri/r0 is found to be almost equal to 0.26, 0.33 and 0.46 corresponding respectively to a low, medium and high friction soil. The results also indicate that the soil dilation angle influences the value of N’c when the soil displays high non-associativity for large internal friction angle values. The computational results are presented in the form of design tables and graphs, and compared with previous published results available in the literature.  相似文献   

19.
Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.  相似文献   

20.
This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (qu) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of qu of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of qu of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

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